We illustrate the MITM attack scheme in Figure REF : a quantum radar (detector) determines on the absence or presence of the target object based on the reflective photon-based quantum states. An attacker blocks the transmission of reflective quantum signals, manipulates them through noisy quantum gates selected from the action space in (REF ), which can be implemented using photonic quantum circuits [1]}, and sends out manipulated quantum signals.
We use the mean number representation to characterize photonic quantum states from the reflective signals [2]}.
We associate the hypotheses \(H_0,H_1\)  with the mixed state of reflective signals under the absence \(H_0\)  or presence \(H_1\)  of the target object in Figure REF , respectively as follows:
\(\begin{aligned}H_0:\rho _0 &= (1-N_B)|0\rangle \langle 0| + N_B{|k\rangle \langle k|},\\H_1: \rho _1 &= (1-x)\left((1-N_B)|0\rangle \langle 0| + N_B{|k\rangle \langle k|}\right) + x|l\rangle \langle l|,\end{aligned}\) 
